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Rates of convergence in some SLLN under weak dependence conditions. (English) Zbl 1240.60060

Based on results of F. Móricz [Z.Wahrscheinlichkeitstheor.Verw.Geb.35, 299–314 (1976; Zbl 0314.60023)] and I. Fazekas and O. Klesov [Theory Probab. Appl. 45, No. 3, 436-449 (2000; Zbl 0991.60021)], the authors develop a general and quite effective method to derive convergence rate results in strong laws of large numbers for partial sums from suitable weighted maximal moment inequalities. The results obtained cover various weakly dependent situations, such as strong mixing cases, causal weak dependence, but also non-causal weak dependence. Moreover, convergence rates for kernel density and regression estimators of Nadaraya-Watson type are obtained via the same technique and also for a number of different dependence situations.

MSC:

60F15 Strong limit theorems
60F99 Limit theorems in probability theory
60G10 Stationary stochastic processes
62G07 Density estimation
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